We discuss the discovery potential of a dark force carrier (Z') of very light mass, mz' <= O(1-10) GeV, at hadron colliders via rare top quark decays, especially when it decays invisibly in typical search schemes. We emphasize that the top sector is promising for the discovery of new particles because top quark pairs are copiously produced at the Large Hadron Collider. The signal process is initiated by a rare top decay into a bottom quark and a charged Higgs boson (H +/-) decaying subsequently into a W and one or multiple Z's. The light Z' can be invisible in collider searches in various scenarios, and it would be hard to distinguish the relevant collider signature from the regular tt process in the Standard Model. We suggest a search strategy using the recently proposed on-shell constrained M-2 variables. Our signal process is featured by an asymmetric event topology, while the t (t) over bar is symmetric. The essence behind the strategy is to evoke some contradiction in the relevant observables by applying the kinematic variables designed under the assumption of the tt event topology. To see the viability of the proposed technique, we perform Monte Carlo simulations including realistic effects such as cuts, backgrounds, detector resolution, and so on at the LHC of root s = 14 TeV.